graph_tool.stats - Graph Statistics

Summary

vertex_hist (g, deg[, bins, float_count])	Return the vertex histogram of the given degree type or property.
edge_hist (g, eprop[, bins, float_count])	Return the edge histogram of the given property.
vertex_average (g, deg)	Return the average of the given degree or vertex property.
edge_average (g, eprop)	Return the average of the given degree or vertex property.
label_parallel_edges (g[, eprop])	Label edges which are parallel, i.e, have the same source and target vertices. For each parallel edge set PE, the labelling starts from 0 to |PE|-1. If the eprop parameter is given (a PropertyMap), the labelling is stored there.
remove_parallel_edges (g)	Remove all parallel edges from the graph. Only one edge from each parallel edge set is left.
label_self_loops (g[, eprop])	Label edges which are self-loops, i.e, the source and target vertices are the same. Self-loops are labeled with 1 and others with 0. If the eprop parameter is given (a PropertyMap), the labelling is stored there.
remove_self_loops (g)	Remove all self-loops edges from the graph.
remove_labeled_edges (g, label)	Remove every edge e such that label[e] != 0.
distance_histogram (g[, weight, bins, samples, ...])	Return the shortest-distance histogram for each vertex pair in the graph.

Contents

graph_tool.stats.vertex_hist(g, deg, bins=[, 1], float_count=True)

Return the vertex histogram of the given degree type or property.

Parameters:

g : Graph

Graph to be used.

deg : string or PropertyMap

Degree or property to be used for the histogram. It can be either “in”, “out” or “total”, for in-, out-, or total degree of the vertices. It can also be a vertex property map.

bins : list of bins

List of bins to be used for the histogram. The values given represent the edges of the bins (i,e, lower bounds). If the list contains only one value, this will be used to automatically create an appropriate bin range, with a constant lenght given by this value.

float_count : bool (optional, default: True)

If True, the counts in each histogram bin will be returned as floats. If False, they will be returned as integers.

Returns:

counts : ndarray

The bin counts.

bins : ndarray

The bin edges.

See also

edge_hist

Edge histograms.

vertex_average

Average of vertex properties, degrees.

edge_average

Average of edge properties.

distance_histogram

Shortest-distance histogram.

Notes

The algorithm runs in O(|V|) time.

If enabled during compilation, this algorithm runs in parallel.

Examples

>>> from numpy.random import poisson, seed
>>> seed(42)
>>> g = gt.random_graph(1000, lambda: (poisson(5), poisson(5)))
>>> print gt.vertex_hist(g, "out")
[array([  10.,   30.,   86.,  138.,  166.,  154.,  146.,  129.,   68.,
         36.,   23.,    8.,    3.,    2.,    0.,    1.]), array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15], dtype=uint64)]

graph_tool.stats.edge_hist(g, eprop, bins=[, 1], float_count=True)

Return the edge histogram of the given property.

Parameters:

g : Graph

Graph to be used.

eprop : PropertyMap

Edge property to be used for the histogram.

bins : list of bins

List of bins to be used for the histogram. The values given represent the edges of the bins (i,e, lower bounds). If the list contains only one value, this will be used to automatically create an appropriate bin range, with a constant lenght given by this value.

float_count : bool (optional, default: True)

If True, the counts in each histogram bin will be returned as floats. If False, they will be returned as integers.

Returns:

counts : ndarray

The bin counts.

bins : ndarray

The bin edges.

See also

vertex_hist

Vertex histograms.

vertex_average

Average of vertex properties, degrees.

edge_average

Average of edge properties.

distance_histogram

Shortest-distance histogram.

Notes

The algorithm runs in O(|E|) time.

If enabled during compilation, this algorithm runs in parallel.

Examples

>>> from numpy import arange
>>> from numpy.random import random, seed
>>> seed(42)
>>> g = gt.random_graph(1000, lambda: (5, 5))
>>> eprop = g.new_edge_property("double")
>>> eprop.get_array()[:] = random(g.num_edges())
>>> print gt.edge_hist(g, eprop, arange(0, 1, 0.1))
[array([ 525.,  504.,  502.,  502.,  468.,  499.,  531.,  471.,  520.,  478.]), array([ 0. ,  0.1,  0.2,  0.3,  0.4,  0.5,  0.6,  0.7,  0.8,  0.9])]

graph_tool.stats.vertex_average(g, deg)

Return the average of the given degree or vertex property.

Parameters:

g : Graph

Graph to be used.

deg : string or PropertyMap

Degree or property to be used for the histogram. It can be either “in”, “out” or “total”, for in-, out-, or total degree of the vertices. It can also be a vertex property map.

Returns:

average : float

The average of the given degree or property.

std : float

The standard deviation of the average.

See also

vertex_hist

Vertex histograms.

edge_hist

Edge histograms.

edge_average

Average of edge properties.

distance_histogram

Shortest-distance histogram.

Notes

The algorithm runs in O(|V|) time.

If enabled during compilation, this algorithm runs in parallel.

Examples

>>> from numpy.random import poisson, seed
>>> seed(42)
>>> g = gt.random_graph(1000, lambda: (poisson(5), poisson(5)))
>>> print gt.vertex_average(g, "in")
(5.0919999999999996, 0.071885575743677543)

graph_tool.stats.edge_average(g, eprop)

Return the average of the given degree or vertex property.

Parameters:

g : Graph

Graph to be used.

eprop : PropertyMap

Edge property to be used for the histogram.

Returns:

average : float

The average of the given property.

std : float

The standard deviation of the average.

See also

vertex_hist

Vertex histograms.

edge_hist

Edge histograms.

vertex_average

Average of vertex degree, properties.

distance_histogram

Shortest-distance histogram.

Notes

The algorithm runs in O(|E|) time.

If enabled during compilation, this algorithm runs in parallel.

Examples

>>> from numpy import arange
>>> from numpy.random import random, seed
>>> seed(42)
>>> g = gt.random_graph(1000, lambda: (5, 5))
>>> eprop = g.new_edge_property("double")
>>> eprop.get_array()[:] = random(g.num_edges())
>>> print gt.edge_average(g, eprop)
(0.49674035434130187, 0.0040946040690938677)

graph_tool.stats.label_parallel_edges(g, eprop=None)

Label edges which are parallel, i.e, have the same source and target vertices. For each parallel edge set PE, the labelling starts from 0 to |PE|-1. If the eprop parameter is given (a PropertyMap), the labelling is stored there.

graph_tool.stats.remove_parallel_edges(g)

Remove all parallel edges from the graph. Only one edge from each parallel edge set is left.

graph_tool.stats.label_self_loops(g, eprop=None)

Label edges which are self-loops, i.e, the source and target vertices are the same. Self-loops are labeled with 1 and others with 0. If the eprop parameter is given (a PropertyMap), the labelling is stored there.

graph_tool.stats.remove_self_loops(g)

Remove all self-loops edges from the graph.

graph_tool.stats.remove_labeled_edges(g, label)

Remove every edge e such that label[e] != 0.

graph_tool.stats.distance_histogram(g, weight=None, bins=[, 1], samples=None, float_count=True)

Return the shortest-distance histogram for each vertex pair in the graph.

Parameters:

g : Graph

Graph to be used.

weight : PropertyMap (optional, default: None)

Edge weights.

bins : list (optional, default: [1])

List of bins to be used for the histogram. The values given represent the edges of the bins (i,e, lower bounds). If the list contains only one value, this will be used to automatically create an appropriate bin range, with a constant length given by this value.

samples : int (optional, default: None)

If supplied, the distances will be randomly sampled from a number of source vertices given by this parameter. It samples == None (default), all pairs are used.

float_count : bool (optional, default: True)

If True, the counts in each histogram bin will be returned as floats. If False, they will be returned as integers.

Returns:

counts : ndarray

The bin counts.

bins : ndarray

The bin edges.

See also

vertex_hist

Vertex histograms.

edge_hist

Edge histograms.

vertex_average

Average of vertex degree, properties.

distance_histogram

Shortest-distance histogram.

Notes

The algorithm runs in O(V^2) time, or O(V^2\log V) if weight != None. If samples is supplied, the complexities are O(\text{samples}\times V) and O(\text{samples}\times V\log V), respectively.

If enabled during compilation, this algorithm runs in parallel.

Examples

>>> from numpy.random import random, seed
>>> seed(42)
>>> g = gt.random_graph(100, lambda: (3, 3))
>>> hist = gt.distance_histogram(g)
>>> print hist
[array([    0.,   300.,   857.,  2186.,  3894.,  2511.,   152.]), array([0, 1, 2, 3, 4, 5, 6], dtype=uint64)]
>>> hist = gt.distance_histogram(g, samples=10)
>>> print hist
[array([   0.,   30.,   88.,  222.,  384.,  251.,   15.]), array([0, 1, 2, 3, 4, 5, 6], dtype=uint64)]